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A Smoother Pebble: Mathematical Explorations
This book takes a novel look at the topics of school mathematics--arithmetic, geometry, algebra, and calculus. In this stroll on the mathematical seashore we hope to find, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This book assembles a collection of mathematical pebbles that are important as well as beautiful.
266 pages, Hardcover
First published January 1, 2003
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Displaying 1 - 2 of 2 reviews
July 9, 2008
"If I have made any valuable discoveries, it has been owing more to paatient attention than to any other talent" - Newton
"The identification of border and wallpaper patterns provides an interesting diversion, especially for bird watchers and wildflower fanciers during the off season." p.158, about the study of symmetry and planar tilings
The Egyptians used mostly only sums of integer reciprocals to represent fractions (allowing also 2/3). So 5/7 = 1/2 + 1/7 + 1/14. This I already knew. What was new for me was one way this is better. Suppose you have 5 pies to be divided equally among 7 people. Instead of chopping each pie into 7ths, you could give person A 5/7 of pie 1, person B 2/7 of pie 1 and 3/7 of pie 2, person C 4/7 of pie 2 and 1/7 of pie 3... But another way is based on the Egyptian fraction: give everyone half a pie, leaving 1 whole and 1 half pie. Cut the whole into 7ths and give everybody a piece, and similarly for the half.
"The identification of border and wallpaper patterns provides an interesting diversion, especially for bird watchers and wildflower fanciers during the off season." p.158, about the study of symmetry and planar tilings
The Egyptians used mostly only sums of integer reciprocals to represent fractions (allowing also 2/3). So 5/7 = 1/2 + 1/7 + 1/14. This I already knew. What was new for me was one way this is better. Suppose you have 5 pies to be divided equally among 7 people. Instead of chopping each pie into 7ths, you could give person A 5/7 of pie 1, person B 2/7 of pie 1 and 3/7 of pie 2, person C 4/7 of pie 2 and 1/7 of pie 3... But another way is based on the Egyptian fraction: give everyone half a pie, leaving 1 whole and 1 half pie. Cut the whole into 7ths and give everybody a piece, and similarly for the half.
April 7, 2016
This is a book that I will always go back to for reference.
Displaying 1 - 2 of 2 reviews